Heretofore, methods for predicting the size and volume of a geologic reservoir and developing and identifying representative images of its boundary limits have relied on seismic and geologic data and classic diffusion theory based upon the hydraulic diffusively of the reservoir's formations. Historically, data plots of reservoir pressure versus a semi-logarithm of well flow time have been used to graphically analyze well flow tests and many such analyses have noted that the plots include abrupt changes in slope of the pressure versus time function and suspected that these abrupt changes have relevance to the reservoir boundaries. These measurements of pressure versus flow-time have been based on two types of conditions. In one, known as the "flow test" or "drawdown", the fluid flow into the well is shut off for an extended period of time until the pressure reaches a steady state, following which the well is allowed to flow at a constant flow rate while the pressure is monitored. Another kind of test is the "shut in" or "buildup" test and is the reverse of the flow test: the reservoir is allowed to flow for an extended period of time until the pressure stabilizes and then the flow is shut off while the pressure is monitored. Yet another kind of test is called an "injection test" in which a borehole fluid is injected into the formation, the injection of fluid is stopped, and the pressure monitored.
Variations on the "flow test" and the "shut in" test include observations at a plurality of wells in a reservoir. In such multiple well observations, for example, one well might be opened up in a flow test while the pressure in a second, shut in, well is monitored. A another example of multiple well observations, one well might be shut in while the pressure in a second, flowing well, is monitored. These are called interference tests.
However, analysts note that while a diffusion theory mathematical model incorporating fixed boundaries or limits provides long smooth functional transitions between pressure-time function slope changes whereas slope changes relating to actual changes in nature in permeability boundaries in geologic formations, are often sharp and abrupt when a reservoir limit is encountered.
Furthermore, attempts at the superposition of infinite acting diffusion equation fields in such analyses have resulted in calculations of a distance d between the well in the reservoir and the reservoir boundary limits have been proven to be very imprecise, such calculations being most often based on the theoretical relationship of d=0.749.sqroot..eta.t where d is the distance from the well to the first limit, .eta. is the hydraulic diffusivity of the formation, and t is the time elapsed from the initiation of well flow. This relationship is based upon a single linear sealing boundary in an infinite reservoir. It has been rigorously derived many times as the projected intersection of the 2:1 slope change in the pressure-time function. Other derivations have given values ranging up to 0.5. It carries through to any model based upon constant flow and the diffusivity equation. The present invention provides a more precise and reliable method for determining the distance d from a reservoir well to each of the reservoir boundary limits as a discrete engineering calculation and for deriving a more representative identification and simulation of the reservoir's boundary limits.